细分生成B样条的几何作图法  

Geometric Construction Method of the Generation of B-splines by Using p-nary Subdivision Scheme

作　　者：郑红婵[1] 叶正麟[1] 赵红星[1] 孟雅琴[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《计算机工程与应用》2005年第26期8-11,共4页Computer Engineering and Applications

基　　金：陕西省自然科学基金项目(编号:2002A20);陕西省教育厅专项科研计划项目(编号:02JK192);西北工业大学博士论文创新基金资助项目(编号:CX200328)

摘　　要：研究均匀B样条曲线细分生成的几何作图问题,给出了采用p-nary细分法细分生成任意次均匀B样条曲线的递归细分算法。在此基础上,研究了任意次均匀B样条曲线p-nary细分生成的几何作图方法。利用这种几何作图法,可以直观地在计算机上通过编程来快速准确地绘制B样曲线,更重要的是,可以使基于几何方法的任意次B样曲线的手工绘制成为可能。Since the de Casteljau algorithm and the de Boor algorithm,the two intuitive geometric construction methods for curves,are very important in the field of curve and surface,in this paper we focus on the geometric construction method of the generation of uniform B-splines of any degree by using p-nary subdivision scheme.We first introduce the p-nary recursive subdivision algorithm of uniform B-splines of any degree.Then we discuss the geometric construction method of the generation of uniform B-splines of arbitrary degree by using p-nary subdivision scheme.Our methods are easy to implement,regardless of degree.Due to the high performance property of p-nary subdivision algorithm,using the methods presented in this paper one can plot uniform B-splines of arbitrary degree effectively and rapidly.

关 键 词：均匀B样条p-nary细分 生成多项式 几何作图 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]